共查询到20条相似文献,搜索用时 31 毫秒
1.
本文首次通过借助Kakutani-Fan-Glicksberg固定点定理和非线性标量化,研究了向量值映射的Benson锥鞍点定理.然后,通过使用该Kakutani-Fan-Glicksberg固定点定理,同样得到了集值映射的锥松鞍点定理. 相似文献
2.
In this paper, by virtue of the separation theorem of convex sets, we prove a minimax theorem, a cone saddle point theorem and a Ky Fan minimax theorem for a scalar set-valued mapping under nonconvex assumptions of its domains, respectively. As applications, we obtain an existence result for the generalized vector equilibrium problem with a set-valued mapping. Simultaneously, we also obtain some generalized Ky Fan minimax theorems for set-valued mappings, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization. 相似文献
3.
Caiyun Jin 《Numerical Functional Analysis & Optimization》2019,40(7):825-843
In this article, an approximate minimax theorem for bi-lower-semicontinuous set-valued mapping was proved, relationships between semicontinuous set-valued mappings are discussed and the existence of approximate maxmin was given. The minimax theorem in this article is the first minimax theorem that doesn’t require the set-valued mappings to be continuous. 相似文献
4.
Xianqiang Luo 《数学研究通讯:英文版》2011,27(3):268-278
In this paper, we establish a fixed point theorem for set-valued mapping
on a topological vector space without "local convexity". And we also establish some
generalized Ky Fan's minimax inequalities for set-value vector mappings, which are
the generalization of some previous results. 相似文献
5.
R. P. Agarwal M. Balaj D. O’Regan 《Journal of Optimization Theory and Applications》2014,163(2):482-490
In this paper, we establish a common fixed point theorem for a family of self set-valued mappings on a compact and convex set in a locally convex topological vector space. As applications, we obtain an existence theorem of solutions for a variational inequality of Stampacchia type and some Ky Fan-type minimax inequalities. 相似文献
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7.
Mircea Balaj 《Applied Mathematics Letters》2010,23(3):241-245
In this paper, using the Brouwer fixed point theorem, we establish a common fixed point theorem for a family of set-valued mappings. As applications of this result we obtain existence theorems for the solutions of two types of vector equilibrium problems, a Ky Fan-type minimax inequality and a generalization of a known result due to Iohvidov. 相似文献
8.
Tomonari Suzuki 《Journal of Mathematical Analysis and Applications》2008,340(1):752-755
We give an example which says that Mizoguchi-Takahashi's fixed point theorem for set-valued mappings is a real generalization of Nadler's. We also give a very simple proof of Mizoguchi-Takahashi's theorem. 相似文献
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10.
Aparna Mehra 《Journal of Mathematical Analysis and Applications》2002,276(2):815-832
In this paper, we establish a scalarization theorem and a Lagrange multiplier theorem for super efficiency in vector optimization problem involving nearly convexlike set-valued maps. A dual is proposed and duality results are obtained in terms of super efficient solutions. A new type of saddle point, called super saddle point, of an appropriate set-valued Lagrangian map is introduced and is used to characterize super efficiency. 相似文献
11.
在这篇文章中我们研究了对于不等式约束的非线性规划问题如何根据极小极大问题的鞍点来找精确罚问题的解。对于一个具有不等式约束的非线性规划问题,通过罚函数,我们构造出一个极小极大问题,应用交换“极小”或“极大”次序的策略,证明了罚问题的鞍点定理。研究结果显示极小极大问题的鞍点是精确罚问题的解。 相似文献
12.
Gu-Sheng Tang Qing-Bang Zhang Cao-Zong Cheng 《Journal of Mathematical Analysis and Applications》2007,334(2):1481-1491
By using basic KKM theorem, a new matching theorem and some minimax inequalities for set-valued mappings defined on the FC-spaces are proved under very weak assumptions. These results generalized many known results from the recent literature. 相似文献
13.
The paper deals with a generalization of a vector quasivariational inequality. An existence theorem for its solutions is established; it is based on a kind of minimax inequality, which is here established for continuous affine mappings and differs from previous results. Fan's section theorem for set-valued mappings is extended. An application for an equilibrium problem of a network with vector-valued cost functions is given.This research was supported by the National Nature Science Foundation of China. 相似文献
14.
Xie Ping DING 《数学学报(英文版)》2007,23(10):1869-1880
In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature. 相似文献
15.
We study the existence of best proximity points for single-valued non-self mappings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric property. Examples are given to support the usability of our results. 相似文献
16.
Moosa GABELEH 《数学物理学报(B辑英文版)》2014,(5):1661-1669
We study the existence of best proximity points for single-valued non-self map-pings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric property. Examples are given to support the usability of our results. 相似文献
17.
Lai-Jiu Lin 《Journal of Global Optimization》2007,38(1):21-39
In this paper, we study an existence theorem of systems of generalized quasivariational inclusions problem. By this result,
we establish the existence theorems of solutions of systems of generalized equations, systems of generalized vector quasiequilibrium
problem, collective variational fixed point, systems of generalized quasiloose saddle point, systems of minimax theorem, mathematical
program with systems of variational inclusions constraints, mathematical program with systems of equilibrium constraints and
systems of bilevel problem and semi-infinite problem with systems of equilibrium problem constraints.
This research was supported by the National Science Council of the Republic of China. 相似文献
18.
近似锥一次类凸集值向量优化问题强有效解的广义鞍点刻画 总被引:1,自引:1,他引:0
本文研究了近似锥一次类凸集值向量优化强有效解的广义鞍点表示问题.利用择一定理,得到了近似锥-次类凸集值优化问题强有效解为广义鞍点的充分条件和必要条件.所得结果丰富了集值优化理论,并且拓广了广义鞍点的应用. 相似文献
19.
研究向量集值映射的拟均衡问题的有效解,利用数值化方法与不动点定理,得到解的存在性定理.作为应用,得到广义向量鞍点,向量变分不等式与向量互补问题的存在性定理. 相似文献
20.
In this paper, minimax theorems and saddle points for a class of vector-valued mappings f(x, y) = u(x)+β(x)v(y) are first investigated in the sense of lexicographic order, where u, v are two general vector-valued mappings and β is a non-negative real-valued function. Then, by applying the existence theorem of lexicographic saddle point, we investigate a lexicographic equilibrium problem and establish an equivalent relationship between the lexicographic saddle point theorem and existence theorem of a lexicographic equilibrium problem for vector-valued mappings. 相似文献